Variable step stiffly stable methods

Abstract

There is much current interest in the problem of devising numerical methods of stiff ODEs. Stiffly stable variable step methods of order 3 and 4 are established. Some stability properties of multistep formulas will be discussed, some theorems and lemmas are proved. A comparison off θ in DRC(θ) of the variable step formulas depends on free parameter for some orders are discussed. This free parameter will be restricted to [-1, 1) with the upper bounds of the step ratios of the formulas. Some numerical results are tabulated.

Keywords:

• Variable step
• stiffly stable
• differential equations
• damped root condition(DRC)

C.R. Categories:

• G.1.7